Question

Use the SAT data and create a multiple regression table but this time as input use ONLY two variables: Letters and SAT. Answer questions 1 to 4. Choose the best fitting answer. Note: numbers are truncated unless specified.

C ollege GPA HighSchl GPA SAT Letters 2.04 2.01 1070 5 2.56 3.4 1254 6 3.75 3.68 1466 6 1.1 1.54 706 4 3 3.32 1160 5 0.05 0.33 756 3 1.38 0.36 1058 2 1.5 1.97 1008 7 1.38 2.03 1104 4 4.01 2.05 1200 7 1.5 2.13 896 7 1.29 1.34 848 3 1.9 1.51 958 5 3.11 3.12 1246 6 1.92 2.14 1106 4 0.81 2.6 790 5 1.01 1.9 954 4 3.66 3.06 1500 6 2 1.6 1046 5 2.05 1.96 1054 4 2.6 1.96 1198 6 2.55 1.56 940 3 0.38 1.6 456 6 2.48 1.92 1150 7 2.74 3.09 636 6 1.77 0.78 744 5 1.61 2.12 644 5 0.99 1.85 842 3 1.62 1.78 852 5 2.03 1.03 1170 3 3.5 3.44 1034 10 3.18 2.42 1202 5 2.39 1.74 1018 5 1.48 1.89 1180 5 1.54 1.43 952 3 1.57 1.64 1038 4 2.46 2.69 1090 6 2.42 1.79 694 5 2.11 2.72 1096 6 2.04 2.15 1114 5 1.68 2.22 1256 6 1.64 1.55 1208 5 2.41 2.34 820 6 2.1 2.92 1222 4 1.4 2.1 1120 5 2.03 1.64 886 4 1.99 2.83 1126 7 2.24 1.76 1158 4 0.45 1.81 676 6 2.31 2.68 1214 7 2.41 2.55 1136 6 2.56 2.7 1264 6 2.5 1.66 1116 3 2.92 2.23 1292 4 2.35 2.01 604 5 2.82 1.24 854 6 1.8 1.95 814 6 1.29 1.73 778 3 1.68 1.08 800 2 3.44 3.46 1424 7 1.9 3.01 950 6 2.06 0.54 1056 3 3.3 3.2 956 8 1.8 1.5 1352 5 2 1.71 852 5 1.68 1.99 1168 5 1.94 2.76 970 6 0.97 1.56 776 4 1.12 1.78 854 6 1.31 1.32 1232 5 1.68 0.87 1140 6 3.09 1.75 1084 4 1.87 1.41 954 2 2 2.77 1000 4 2.39 1.78 1084 4 1.5 1.34 1058 4 1.82 1.52 816 5 1.8 2.97 1146 7 2.01 1.75 1000 6 1.88 1.64 856 4 1.64 1.8 798 4 2.42 3.37 1324 6 0.22 1.15 704 6 2.31 1.72 1222 5 0.95 2.27 948 6 1.99 2.85 1182 8 1.86 2.21 1000 6 1.79 1.94 910 6 3.02 4.25 1374 9 1.85 1.83 1014 6 1.98 2.75 1420 7 2.15 1.71 400 6 1.46 2.2 998 7 2.29 2.13 776 6 2.39 2.38 1134 7 1.8 1.64 772 4 2.64 1.87 1304 6 2.08 2.53 1212 4 0.7 1.78 818 6 0.89 1.2 864 2

1. If an incoming student has a letter score = 8 and SAT = 1300 what would his predicted College GPA be? a. 1.84 b. 2.65 c. ​​2.93 d. 2.79

2. What is the approximate error of this prediction? a. 0.61 b. ​​0.63 c. 0.57 d. 0.33

3. If this student decreases his SAT by 150 points how much would the student's predicted college GPA change? a. 0.46 b. - 0.24 c. 0.33 d. - 0.54

4. If two students have the identical SAT but one has a Letter score 1 points higher than the other, how much higher will his College GPA be? a. It will be the same. b. 0.12 c. 0.0012 d. 0.001

Answer 1

1. If an incoming student has a letter score = 8 and SAT = 1300 what would his predicted College GPA be?

d. 2.79

2. What is the approximate error of this prediction?

a. 0.61

3. If this student decreases his SAT by 150 points how much would the student's predicted college GPA change?

b. - 0.24

4. If two students have the identical SAT but one has a Letter score 1 points higher than the other, how much higher will his College GPA be?

b. 0.12

The regression output is:

	R²	0.332
	Adjusted R²	0.318
	R	0.576
	Std. Error	0.619
	n	100
	k	2
	Dep. Var.	College GPA
ANOVA table
Source	SS	df	MS	F	p-value
Regression	18.44455387	2	9.22227694	24.09	3.20E-09
Residual	37.12812113	97	0.38
Total	55.57267500	99
Regression output					confidence interval
variables	coefficients	std. error	t (df=97)	p-value	95% lower	95% upper
Intercept	-0.3043
SAT	0.0016	0.00029311	5.513	2.91E-07	0.0010	0.0022
Letters	0.1243	0.0426	2.918	.0044	0.0397	0.2088
Predicted values for: College GPA
			95% Confidence Interval		95% Prediction Interval
SAT	Letters	Predicted	lower	upper	lower	upper	Leverage
1,300	8	2.79	2.50450	3.07687	1.52987	4.05150	0.054

The data is:

College GPA	High Schl GPA	SAT	Letters
2.04	2.01	1070	5
2.56	3.4	1254	6
3.75	3.68	1466	6
1.1	1.54	706	4
3	3.32	1160	5
0.05	0.33	756	3
1.38	0.36	1058	2
1.5	1.97	1008	7
1.38	2.03	1104	4
4.01	2.05	1200	7
1.5	2.13	896	7
1.29	1.34	848	3
1.9	1.51	958	5
3.11	3.12	1246	6
1.92	2.14	1106	4
0.81	2.6	790	5
1.01	1.9	954	4
3.66	3.06	1500	6
2	1.6	1046	5
2.05	1.96	1054	4
2.6	1.96	1198	6
2.55	1.56	940	3
0.38	1.6	456	6
2.48	1.92	1150	7
2.74	3.09	636	6
1.77	0.78	744	5
1.61	2.12	644	5
0.99	1.85	842	3
1.62	1.78	852	5
2.03	1.03	1170	3
3.5	3.44	1034	10
3.18	2.42	1202	5
2.39	1.74	1018	5
1.48	1.89	1180	5
1.54	1.43	952	3
1.57	1.64	1038	4
2.46	2.69	1090	6
2.42	1.79	694	5
2.11	2.72	1096	6
2.04	2.15	1114	5
1.68	2.22	1256	6
1.64	1.55	1208	5
2.41	2.34	820	6
2.1	2.92	1222	4
1.4	2.1	1120	5
2.03	1.64	886	4
1.99	2.83	1126	7
2.24	1.76	1158	4
0.45	1.81	676	6
2.31	2.68	1214	7
2.41	2.55	1136	6
2.56	2.7	1264	6
2.5	1.66	1116	3
2.92	2.23	1292	4
2.35	2.01	604	5
2.82	1.24	854	6
1.8	1.95	814	6
1.29	1.73	778	3
1.68	1.08	800	2
3.44	3.46	1424	7
1.9	3.01	950	6
2.06	0.54	1056	3
3.3	3.2	956	8
1.8	1.5	1352	5
2	1.71	852	5
1.68	1.99	1168	5
1.94	2.76	970	6
0.97	1.56	776	4
1.12	1.78	854	6
1.31	1.32	1232	5
1.68	0.87	1140	6
3.09	1.75	1084	4
1.87	1.41	954	2
2	2.77	1000	4
2.39	1.78	1084	4
1.5	1.34	1058	4
1.82	1.52	816	5
1.8	2.97	1146	7
2.01	1.75	1000	6
1.88	1.64	856	4
1.64	1.8	798	4
2.42	3.37	1324	6
0.22	1.15	704	6
2.31	1.72	1222	5
0.95	2.27	948	6
1.99	2.85	1182	8
1.86	2.21	1000	6
1.79	1.94	910	6
3.02	4.25	1374	9
1.85	1.83	1014	6
1.98	2.75	1420	7
2.15	1.71	400	6
1.46	2.2	998	7
2.29	2.13	776	6
2.39	2.38	1134	7
1.8	1.64	772	4
2.64	1.87	1304	6
2.08	2.53	1212	4
0.7	1.78	818	6
0.89	1.2	864	2